{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import inv\n",
    "from scipy.stats import multivariate_normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = \"retina\"\n",
    "plt.rcParams[\"axes.spines.right\"] = False\n",
    "plt.rcParams[\"axes.spines.top\"] = False\n",
    "np.set_printoptions(precision=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we are given a dataset $\\mathcal{D}=\\left\\{({\\bf x}_n, y_n)\\vert {\\bf x}_n \\in \\mathbb{R}^M, y_n\\in\\mathbb{R} \\right\\}_{n=1}^N$. Where each element $y_n$ is modelled as\n",
    "\n",
    "\n",
    "$$\n",
    "    y_n\\vert {\\bf x}_n \\sim \\mathcal{N}({\\bf w}^T{\\bf x}, \\sigma^2)\n",
    "$$\n",
    "\n",
    "Furthermore, we we assign $\\bf w$ a *prior* distribution of the form ${\\bf w}\\sim\\mathcal{N}(\\boldsymbol\\mu_0, \\boldsymbol\\Sigma_0)$. Our goal is to find the *posterior* distribution ${\\bf w}\\vert \\mathcal{D}$, i.e.,\n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "p({\\bf w}\\vert \\mathcal{D}) &\\propto p({\\bf w})p(\\mathcal D\\vert {\\bf w})\\\\\n",
    "&= \\mathcal{N}({\\bf w}\\vert \\boldsymbol\\mu_0, \\boldsymbol\\Sigma_0) \\mathcal{N}({\\bf y} \\vert {\\bf X}{\\bf w}, \\sigma^2{\\bf I})\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "To find the posterior conjugate (a closed-form solution), note that\n",
    "\n",
    "$$\n",
    "    {\\bf z}^T{\\bf A}{\\bf z} - 2{\\bf z}^T{\\bf b} + c = ({\\bf z} - {\\bf A}^{-1}{\\bf b})^T{\\bf A}({\\bf z} - {\\bf A}^{-1}{\\bf b}) - {\\bf b}^T{\\bf A}^{-1}{\\bf b} + c\n",
    "$$\n",
    "\n",
    "Then,\n",
    "$$\n",
    "\\begin{align}\n",
    "    p({\\bf w}\\vert \\mathcal{D}) &\\propto \\exp\\left(-\\frac{1}{2} ({\\bf w} - \\boldsymbol\\mu_0)^T\\Sigma_0^{-1}({\\bf w} - \\boldsymbol\\mu_0) -\\frac{1}{2\\sigma^2} ({\\bf y} - {\\bf X w})^T({\\bf y} - {\\bf X w}) \\right)\\\\\n",
    "    &= \\exp\\left(-\\frac{1}{2}\\left( ({\\bf w} - \\boldsymbol\\mu_0)^T\\Sigma_0^{-1}({\\bf w} - \\boldsymbol\\mu_0) +\\frac{1}{\\sigma^2} ({\\bf y} - {\\bf X w})^T({\\bf y} - {\\bf X w})\\right) \\right)\\\\\n",
    "    &\\propto \\exp\\left(-\\frac{1}{2}\\left[{\\bf w}^T \\left(\\boldsymbol\\Sigma_0^{-1} + \\frac{1}{\\sigma^2}{\\bf X}^T{\\bf X}\\right) - 2{\\bf w}^T \\left(\\boldsymbol\\Sigma_0^{-1}\\boldsymbol\\mu_0 + \\frac{1}{\\sigma^2}{\\bf X}^T{\\bf y}\\right) \\right]\\right)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "This last expression reduces to\n",
    "\n",
    "$$\n",
    "    p({\\bf w}\\vert \\mathcal{D}) \\propto \\exp\\left(-\\frac{1}{2}({\\bf w} - {\\bf m}_N)^T {\\bf S}_N^{-1} ({\\bf w} - {\\bf m}_N)\\right)\n",
    "$$\n",
    "\n",
    "Where\n",
    "* ${\\bf S}_N^{-1} = \\boldsymbol\\Sigma_0^{-1} + \\frac{1}{\\sigma^2}{\\bf X}^T{\\bf X}$\n",
    "* ${\\bf m}_N = {\\bf S}_N \\left(\\boldsymbol\\Sigma_0^{-1}\\boldsymbol\\mu_0 + \\frac{1}{\\sigma^2}{\\bf X}^T{\\bf y}\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using a bayesian perspective, there does not exist *a* vector of weights $\\bf w$; rather, $\\bf w$ is a random variable that we can sample from."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9dd12f4b20>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 370
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(314)\n",
    "\n",
    "n_obs = 20\n",
    "# sigma is a known value\n",
    "sigma = 0.8\n",
    "x = np.linspace(-1.3, 1.7, n_obs) + np.random.rand(n_obs) * 0.1\n",
    "y = 1 - 3 * x - 2 * x ** 2 + 2.5 * x ** 3 + np.random.randn(n_obs) * sigma\n",
    "\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.0000e+00, -1.2083e+00,  1.4600e+00, -1.7642e+00],\n",
       "       [ 1.0000e+00, -1.0833e+00,  1.1734e+00, -1.2711e+00],\n",
       "       [ 1.0000e+00, -9.5771e-01,  9.1720e-01, -8.7841e-01],\n",
       "       [ 1.0000e+00, -7.4800e-01,  5.5950e-01, -4.1850e-01],\n",
       "       [ 1.0000e+00, -5.7662e-01,  3.3249e-01, -1.9172e-01],\n",
       "       [ 1.0000e+00, -4.2779e-01,  1.8300e-01, -7.8288e-02],\n",
       "       [ 1.0000e+00, -2.7984e-01,  7.8308e-02, -2.1914e-02],\n",
       "       [ 1.0000e+00, -1.6869e-01,  2.8456e-02, -4.8002e-03],\n",
       "       [ 1.0000e+00,  5.4334e-02,  2.9522e-03,  1.6041e-04],\n",
       "       [ 1.0000e+00,  1.4713e-01,  2.1647e-02,  3.1848e-03],\n",
       "       [ 1.0000e+00,  3.5558e-01,  1.2644e-01,  4.4960e-02],\n",
       "       [ 1.0000e+00,  4.6300e-01,  2.1436e-01,  9.9250e-02],\n",
       "       [ 1.0000e+00,  6.0697e-01,  3.6841e-01,  2.2361e-01],\n",
       "       [ 1.0000e+00,  7.9123e-01,  6.2605e-01,  4.9535e-01],\n",
       "       [ 1.0000e+00,  9.9453e-01,  9.8910e-01,  9.8369e-01],\n",
       "       [ 1.0000e+00,  1.0962e+00,  1.2017e+00,  1.3174e+00],\n",
       "       [ 1.0000e+00,  1.2333e+00,  1.5210e+00,  1.8759e+00],\n",
       "       [ 1.0000e+00,  1.4475e+00,  2.0953e+00,  3.0330e+00],\n",
       "       [ 1.0000e+00,  1.6006e+00,  2.5619e+00,  4.1005e+00],\n",
       "       [ 1.0000e+00,  1.7581e+00,  3.0910e+00,  5.4344e+00]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.stack((np.ones_like(x), x, x ** 2, x ** 3), axis=1)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "α = 1.2\n",
    "m = 4\n",
    "Σ0 = np.eye(m) * α\n",
    "μ0 = np.zeros((m, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.794 ],\n",
       "       [-2.7186],\n",
       "       [-1.6215],\n",
       "       [ 2.1555]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SN_inv = inv(Σ0) + X.T @ X / sigma ** 2\n",
    "SN = inv(SN_inv)\n",
    "\n",
    "mN = SN @ (inv(Σ0) @ μ0 + X.T @ y[:, None] / sigma ** 2)\n",
    "# The vector of average weights\n",
    "mN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_test = 100\n",
    "xtest = np.linspace(-1.3, 1.8, n_test)\n",
    "Xtest = np.stack((np.ones_like(xtest), xtest, xtest ** 2, xtest ** 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples = 20\n",
    "# We create an instance of our random vector w\n",
    "w = multivariate_normal(mean=mN.ravel(), cov=SN)\n",
    "w_sample = w.rvs(n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 265,
       "width": 370
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_test_sample = np.einsum(\"km,mn->nk\", w_sample, Xtest)\n",
    "\n",
    "plt.plot(xtest, y_test_sample, c=\"tab:gray\", alpha=0.5, zorder=1)\n",
    "plt.scatter(x, y, c=\"tab:red\", zorder=2)\n",
    "plt.title(\"Posterior Samples\", fontsize=15);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
